Journal ArticleDOI
Thin elastic and periodic plates
D. Caillerie,Jean-Claude Nédélec +1 more
TLDR
In this article, a three dimensional model of elastic periodic plate when the thickness e of the plate and the size ω of the periods are small is studied and convergence proof is carried out.Abstract:
This paper is devoted to the study of a three dimensional model of elastic periodic plate when the thickness e of the plate and the size ω of the periods are small. In the three studied limits (e 0 then ω 0), (ω 0 then e 0) and lately (e and ω 0 together) the three dimensional equation of elasticity are approached by the two dimensional general equations of a linear anisotropic plate, the stretching and bending being coupled. This study points out the importance of the ratio of the two small parameters, indeed the moduli occuring in the two dimensional equations are different in the three limits. In each case a convergence proof is carried out.read more
Citations
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A new model for thin plates with rapidly varying thickness
Robert V. Kohn,Michael Vogelius +1 more
TL;DR: In this paper, the bending of a thin plate with rapidly varying thickness was studied and a fourth-order equation for the midplanc displacement was derived using an asymptotic analysis based on 3D linear elasticity.
Journal ArticleDOI
Asymptotic Homogenization of Composite Materials and Structures
TL;DR: In this article, a review of the state-of-the-art in asymptotic homogenization of composites is presented, by presenting the variety of existing methods, by pointing out their advantages and shortcomings, and by discussing their applications.
Journal ArticleDOI
Homogenization of corrugated core sandwich panels
TL;DR: In this paper, the effective properties of corrugated core sandwich panels are investigated, based on the asymptotic expansion method, and an equivalent Reissner-Mindlin homogeneous plate is derived.
Journal ArticleDOI
Analysis of masonry structures: review of and recent trends in homogenization techniquesThis article is one of a selection of papers published in this Special Issue on Masonry.
Paulo B. Lourenço,Paulo B. Lourenço,Paulo B. Lourenço,Gabriele Milani,Gabriele Milani,Gabriele Milani,Antonio Tralli,Antonio Tralli,Antonio Tralli,Alberto Zucchini,Alberto Zucchini,Alberto Zucchini +11 more
TL;DR: This paper addresses different homogenization techniques available in published literature, aiming at defining a first catalogue and at discussing the advantages and disadvantages of the different approaches.
References
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Journal ArticleDOI
A justification of a nonlinear model in plate theory
TL;DR: In this article, the first term in the expansion is a solution of a known bi-dimensional model in nonlinear plate theory, and the existence of the second term is also established.
Journal ArticleDOI
Two-dimensional approximations of three-dimensional eigenvalue problems in plate theory
Philippe G. Ciarlet,S. Kesavan +1 more
TL;DR: In this article, the eigenvalues and eigenfunctions corresponding to the three-dimensional equations for the linear elastic equilibrium of a clamped plate of thickness 2 ϵ, are shown to converge (in a specific sense) to the 2-dimensional biharmonic operator of plate theory, as ϵ approaches zero.